flights with separate airline/booking

Hi
Does the 72 hour transit have to be flown with the same airline and within the same booking?
Let me clarify:
For example I am hoping to visit Hong Kong from London later this year and was thinking of breaking my journey in Beijing for 2 or 3 days using the visa free transit. The route I am looking to book is to fly out to hong kong from London with a standard 2 hour transit in Beijing airport and then fly back from Beijing direct to London 9 days later, and book a separate flight for day 6 or 7 from hong kong to Beijing, probably with a different airline to the original flights to/from London? Would I still qualify for the free transit in this case? Obviously on arrival in Beijing from Hong Kong I would have a flight to a third region departing 2/3 days later so I'm hoping this would still be ok...